On the classification of elliptic foliations induced by real quadratic fields with center

Liliana Puchuri, Orestes Bueno

Producción científica: Contribución a una revistaArtículorevisión exhaustiva


Related to the study of Hilbert's infinitesimal problem, is the problem of determining the existence and estimating the number of limit cycles of the linear perturbation of Hamiltonian fields. A classification of the elliptic foliations in the projective plane induced by the fields obtained by quadratic fields with center was already studied by several authors. In this work, we devise a unified proof of the classification of elliptic foliations induced by quadratic fields with center. This technique involves using a formula due to Cerveau & Lins Neto to calculate the genus of the generic fiber of a first integral of foliations of these kinds. Furthermore, we show that these foliations induce several examples of linear families of foliations which are not bimeromorphically equivalent to certain remarkable examples given by Lins Neto.
Idioma originalEspañol
Páginas (desde-hasta)7157-7193
Número de páginas37
PublicaciónJournal of Differential Equations
EstadoPublicada - 15 dic. 2016

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